SOLUTION: Hello, How can I find {{{a[1]}}} and d if {{{ a[4]=16 }}} and {{{ s[15]=420 }}} ? I am not sure which formula to use. Thanks so much.

Algebra ->  Sequences-and-series -> SOLUTION: Hello, How can I find {{{a[1]}}} and d if {{{ a[4]=16 }}} and {{{ s[15]=420 }}} ? I am not sure which formula to use. Thanks so much.      Log On


   

Question 944285: Hello,
How can I find a%5B1%5D and d if
+a%5B4%5D=16+ and +s%5B15%5D=420++ ?
I am not sure which formula to use.
Thanks so much.
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a[4]=16 and s[15]=420
-------------
Equations:
a(1) + 3d = 16
a(1) + 14d = 420
-----
Subtract and solve for "d"::
11d = 404
d = 404/11
-----
Solve for a(1)::
a(1) + 3(404/11) = 16
a(1) = 16 - 1212/11
a(1) = 176/11 - 1212/11
a(1) = -1036/11
==================
Cheers,
Stan H.
------------------

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
How can I find a%5B1%5D and d if
+a%5B4%5D=16+ and +s%5B15%5D=420++ ?
I am not sure which formula to use.
Thanks so much.
Use the "term" formula to create an equation in the 2 variables, a%5B1%5D and d

Term formula: a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d

Use the "sum of terms" formula to create an equation in the 2 variables, a%5B1%5D and d

Sum of terms formula: S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29



From the 2 equations just formed, solve for the 2 variables, a%5B1%5D and d



You should get: 1st term, or highlight_green%28a%5B1%5D+=+7%29  

You should get: common difference, or highlight_green%28d+=+3%29   

Then do a check!! 

===================

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